Elements of Algebraic Coding Systems

Elements of Algebraic Coding Systems is an introductory textto algebraic coding theory. In the first chapter you'll gain insideknowledge of coding fundamentals which is essential for a deeperunderstanding of state-of-the-art coding systems.This book is a quick reference for those who are unfamiliar withthis topic as well as for use with specific applications such as cryptographyand communication. Linear error-correcting block codesthrough elementary principles span eleven chapters of the text.Cyclic codes some finite field algebra Goppa codes algebraic decodingalgorithms and applications in public-key cryptography andsecret-key cryptography are discussed including problems and solutionsat the end of each chapter. Three appendices cover the Gilbertbound and some related derivations a derivation of the Mac-Williams' identities based on the probability of undetected errorand two important tools for algebraic decoding-namely the finitefield Fourier transform and the Euclidean algorithm for polynomials.